Biological models: measuring variability with classical and quantum information

This essay proposes methods to analyse the variability of biological data. The idea is to express the state of a biological system as a linear combination of base states in a Hilbert space. Coefficients of the linear combination can be interpreted as probabilities and informational entropy is associated to each state allowing the definition of a classical variability measure. Besides, state transition matrices can also be calculated and their norms express the dynamics of the system organization and a quantum variability measure. As the examples show, the classical measure expresses a structural variability and the quantum measure expresses a functional variability.     

Zipf's law organizes a psychiatric ward.

We developed a simple mathematical model based on power law fitting for describing the interactions among patients from a psychiatric ward. First we defined a protocol in order to evaluate in a quantative way the state of the patient, measuring sociability/restlessness through a daily analysis of the behavior and attributing a grade for both parameters, per patient. The grades were checked by two different specialists and a table of incidence was constructed. This table generated power laws for the grades and their variations. We concluded that power laws, like Zipf's law, may be good to explain the data, showing a self-organizing process that indicates a strong interaction component determining the whole behavior. We would like to see more data being collected, in other centers and among normal populations, trying to quantify complex collective behavioral phenomena using self-organizing criticality laws.     

Increase in regularity of fetal heart rate variability with age.

It is generally assumed that fetal heart rate variability increases with gestation, reflecting prenatal development of the autonomic nervous system. We examined standard measures quantifying fetal heart rate variability, as well as a complexity measure, approximate entropy, in 66 fetal magnetocardiograms recorded from 22 healthy pregnant women between the 16th and 42nd week of gestation. In particular, regularity in the fetal RR interval time series was assessed on the basis of symbolic dynamics. The results showed that, beside an overall increase in fetal heart rate variability and complexity during pregnancy, there was also an increase in specific sets of binary patterns with low approximate entropy, i.e., a high degree of regularity. These sets were characterized by short epochs of heart rate acceleration and deceleration, and comparison with surrogate data confirmed that their random occurrence is rare. The results most likely reflect the influence of increasingly differentiated fetal behavioral states and transitions between them in association with fetal development.     

N-player quantum games in an EPR setting

The N-player quantum games are analyzed that use an Einstein-Podolsky-Rosen (EPR) experiment, as the underlying physical setup. In this setup, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for N-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the players' payoffs and mixed Nash equilibrium are determined. Players' N x N payoff matrices are then defined using linear functions so that common two-player games can be easily extended to the N-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners' Dilemma game for general N ≥ 2. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs. By dispensing with the standard unitary transformations on state vectors in Hilbert space and using instead rotors and multivectors, based on Clifford's geometric algebra (GA), it is shown how the N-player case becomes tractable. The new mathematical approach presented here has wide implications in the areas of quantum information and quantum complexity, as it opens up a powerful way to tractably analyze N-partite qubit interactions.     

Variability of estimated binding parameters

The standard deviation is often used as a measure of the accuracy or reliability of estimated binding parameters and this implies that the parameter values are normally distributed. This may not be the case and we show that the unknown distribution of acceptable parameter values associated with a specific model and a particular set of experimental data can be calculated easily. This can be done for any binding model, linear or non-linear, and the method is very robust and accurate. The effect of the magnitude of the experimental error and the distribution of data points on the variability of the parameters is readily investigated. This makes the method useful for the practical design of experiments in terms of the number and range of concentrations (or doses) which need to be studied in order to obtain the desired accuracy.     

Modeling animals' behavioral response by Markov chain models for capture-recapture experiments

A bivariate Markov chain approach that includes both enduring (long-term) and ephemeral (short-term) behavioral effects in models for capture-recapture experiments is proposed. The capture history of each animal is modeled as a Markov chain with a bivariate state space with states determined by the capture status (capture/noncapture) and marking status (marked/unmarked). In this framework, a conditional-likelihood method is used to estimate the population size and the transition probabilities. The classical behavioral model that assumes only an enduring behavioral effect is included as a special case of the bivariate Markovian model. Another special case that assumes only an ephemeral behavioral effect reduces to a univariate Markov chain based on capture/noncapture status. The model with the ephemeral behavioral effect is extended to incorporate time effects; in this model, in contrast to extensions of the classical behavioral model, all parameters are identifiable. A data set is analyzed to illustrate the use of the Markovian models in interpreting animals' behavioral response. Simulation results are reported to examine the performance of the estimators.     

Kinematic variability in running: a caution regarding use of the spanning set measure

The spanning set technique quantifies intertrial variability as the span between polynomial curves representing upper and lower standard deviation curves of a repeated movement. This study aimed to assess the validity of the spanning set technique in quantifying variability and specifically to determine its sensitivity to variability presented at different phases of a movement cycle. Knee angle data were recorded from a male participant completing 12 overground running trials. Variability was added to each running trial at five different phases of the running stride. Ten variability magnitudes were also used to assess the effect of variability magnitude on the spanning set measure. Variability was quantified in all trials using mean deviation and the spanning set measure. Results of a repeated-measures ANOVA showed significant differences between the spanning set score for trials using different phases of added variability. In contrast, mean deviation values showed no difference related to the phase of added variability. Therefore, the spanning set technique cannot be recommended as a valid measure of intertrial movement variability.     

Gaussian mixture model of heart rate variability

Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters.     

Quantum-like model of brain's functioning: decision making from decoherence

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (representing mental states). This equilibrium state determines Alice's mixed (i.e., probabilistic) strategy. We use a master equation in which quantum physics describes the process of decoherence as the result of interaction with environment. Thus our model is a model of thinking through decoherence of the initially pure mental state. Decoherence is induced by the interaction with memory and the external mental environment. We study (numerically) the dynamics of quantum entropy of Alice's mental state in the process of decision making. We also consider classical entropy corresponding to Alice's choices. We introduce a measure of Alice's diffidence as the difference between classical and quantum entropies of Alice's mental state. We see that (at least in our model example) diffidence decreases (approaching zero) in the process of decision making. Finally, we discuss the problem of neuronal realization of quantum-like dynamics in the brain; especially roles played by lateral prefrontal cortex or/and orbitofrontal cortex.     

T4 phage evolution data in terms of a time-dependent Topal-Fresco mechanism

A physical interpretation of the Topal-Fresco [Nature 263, 285 (1976)] model for spontaneous base substitutions suggests that hydrogen-bonded DNA protons satisfy the criteria for a classical noninteracting isolated system. Accessible states for duplex G-C protons include the keto-amino state and the six complementary enol-imine isomers. Hydrogen-bonded enol and imine protons occupy symmetric double-minima created by the two sets of indistinguishable electron lone pairs and a single proton belonging to each enol-imine end group. These protons will consequently participate in coupled quantum mechanical flip-flop, tunneling back and forth between symmetric energy wells. This results in a quantum mixing of proton energy states where the lowest energy state will be a linear combination of available G-C isomers. The resulting conclusion is that metastable keto-amino G-C protons will populate accessible enol-imine stationary states at rates governed by quantum laws of statistical equilibrium, consistent with achieving the lowest energy condition for duplex G-C protons. Enol-imine G-C stationary states are bound more tightly, of the order of 3 to 12 kcal/mol, which requires a modified mode of Topal-Fresco replication that will inhibit reequilibration of enol and imine G and C template isomers and, thus, promote the formation of complementary mispairs. The model is demonstrated on time-dependent base substitutions expressed by T4 phage DNA systems where data are consistent with model explanations, including the prediction that time-dependent evolutionary transversion sites will exhibit both G-C-to-T-A and G-C-to-C-G transversions at replication, due to proton flip-flop alteration of G template genetic specificity. The observation that A-T sites are resistant to time-dependent evolutionary base substitutions, expressed exclusively at G-C sites, allows codons to be classified as either evolutionary sensitive (16 codons) or evolutionary resistant (8 codons). These criteria provide possible explanations for expansion properties of the CGG fragile X sequences. Enol-imine G-C stationary states appear to have been misdiagnosed as deamination of cytosine and oxidation of guanine to 8-hydroxyguanine.     

Algorithms for the de novo sequencing of peptides from tandem mass spectra

Proteomics is the study of proteins, their time- and location-dependent expression profiles, as well as their modifications and interactions. Mass spectrometry is useful to investigate many of the questions asked in proteomics. Database search methods are typically employed to identify proteins from complex mixtures. However, databases are not often available or, despite their availability, some sequences are not readily found therein. To overcome this problem, de novo sequencing can be used to directly assign a peptide sequence to a tandem mass spectrometry spectrum. Many algorithms have been proposed for de novo sequencing and a selection of them are detailed in this article. Although a standard accuracy measure has not been agreed upon in the field, relative algorithm performance is discussed. The current state of the de novo sequencing is assessed thereafter and, finally, examples are used to construct possible future perspectives of the field.     

An Emergency Psychiatric Service in a General Hospital

The same extensive range of general hospital facilities should be allocated to emergency psychiatric illness as are available for other medical conditions. During the study herein reported, for every three medical consultations in the emergency ward of a large general hospital, two psychiatric consultations were requested. Over a two-year period when 24-hour coverage by psychiatric consultants was instituted, such assessments increased from 148 to 340 (during the first four months of each year); the increase in police referrals was outstanding, rising from 16 to 105. The general wards of the hospital assumed greater responsibility for further medical treatment, while committal to the mental hospital declined. Many more psychiatric patients could have been treated in the general hospital if facilities had been available. The development of an emergency psychiatric service is not an easy process and co-ordination with other psychiatric resources is required. Residents in training face situations in the emergency ward which are not encountered in any other aspect of their clinical experience.     

The periodicities in and biometeorological relationships with bed occupancy of an acute psychiatric ward in Antwerp,Belgium

Recently, some investigators have established a seasonal pattern in normal human psychology, physiology and behaviour, and in the incidence of psychiatric psychopathology. In an attempt to elucidate the chronopsy and meteotropism in the latter, we have examined the chronograms of, and the biometeorological relationships to bed occupancy of the psychiatric ward of the Antwerp University Hospital during three consecutive calendar years (1987–1989). Weather data for the vicinity were provided by a local meteorological station and comprise mean atmospheric pressure, air temperature, relative humidity, wind speed and minutes of sunlight and precipitation/day. The number of psychiatric beds occupied during the study period exhibited a significant seasonal variation. Peaks in bed occupancy were observed in March and November, with lows in August. An important part of the variability in the number of beds occupied could be explained by the composite effects of weather variables of the preceding weeks. Our results suggest that short-term fluctuations in atmospheric activity may dictate some of the periodicities in psychiatric psychopathology.     

The biomedical standardization of premenstrual syndrome

This essay traces the history of premenstrual syndrome (PMS) in French, British, and American medical literature from 1950 to 2004. Aetiological theories, treatments and diagnostic criteria have varied over time and place, reflecting local conditions and changing notions of objectivity and evidence. During the 1970s researchers in each nation utilised different research strategies to overcome variation and contradictory results characteristic of PMS research. Since the 1980s, attempts have been made to standardise research internationally through prospective daily rating questionnaires that diagnose and measure PMS. Amidst controversy, a psychiatric reformulation of the syndrome was included in the Diagnostic and Statistical Manual of Mental Disorders (DSM). While the diagnostic criteria for this psychiatric category, now called premenstrual dysphoric disorder (PMDD), are widely accepted for research purposes, efforts to transfer them to medical practice have been less successful. PMDD remains a contested disease construct.     

Algorithms for the de novo sequencing of peptides from tandem mass spectra

Proteomics is the study of proteins, their time- and location-dependent expression profiles, as well as their modifications and interactions. Mass spectrometry is useful to investigate many of the questions asked in proteomics. Database search methods are typically employed to identify proteins from complex mixtures. However, databases are not often available or, despite their availability, some sequences are not readily found therein. To overcome this problem, de novo sequencing can be used to directly assign a peptide sequence to a tandem mass spectrometry spectrum. Many algorithms have been proposed for de novo sequencing and a selection of them are detailed in this article. Although a standard accuracy measure has not been agreed upon in the field, relative algorithm performance is discussed. The current state of the de novo sequencing is assessed thereafter and, finally, examples are used to construct possible future perspectives of the field.     

A generative model for measuring latent timing structure in motor sequences

Motor variability often reflects a mixture of different neural and peripheral sources operating over a range of timescales. We present a statistical model of sequence timing that can be used to measure three distinct components of timing variability: global tempo changes that are spread across the sequence, such as might stem from neuromodulatory sources with widespread influence; fast, uncorrelated timing noise, stemming from noisy components within the neural system; and timing jitter that does not alter the timing of subsequent elements, such as might be caused by variation in the motor periphery or by measurement error. In addition to quantifying the variability contributed by each of these latent factors in the data, the approach assigns maximum likelihood estimates of each factor on a trial-to-trial basis. We applied the model to adult zebra finch song, a temporally complex behavior with rich structure on multiple timescales. We find that individual song vocalizations (syllables) contain roughly equal amounts of variability in each of the three components while overall song length is dominated by global tempo changes. Across our sample of syllables, both global and independent variability scale with average length while timing jitter does not, a pattern consistent with the Wing and Kristofferson (1973) model of sequence timing. We also find significant day-to-day drift in all three timing sources, but a circadian pattern in tempo only. In tests using artificially generated data, the model successfully separates out the different components with small error. The approach provides a general framework for extracting distinct sources of timing variability within action sequences, and can be applied to neural and behavioral data from a wide array of systems.     

Automated,Quantitative Cognitive/Behavioral Screening of Mice: For Genetics,Pharmacology, Animal Cognition and Undergraduate Instruction

We describe a high-throughput, high-volume, fully automated, live-in 24/7 behavioral testing system for assessing the effects of genetic and pharmacological manipulations on basic mechanisms of cognition and learning in mice. A standard polypropylene mouse housing tub is connected through an acrylic tube to a standard commercial mouse test box. The test box has 3 hoppers, 2 of which are connected to pellet feeders. All are internally illuminable with an LED and monitored for head entries by infrared (IR) beams. Mice live in the environment, which eliminates handling during screening. They obtain their food during two or more daily feeding periods by performing in operant (instrumental) and Pavlovian (classical) protocols, for which we have written protocol-control software and quasi-real-time data analysis and graphing software. The data analysis and graphing routines are written in a MATLAB-based language created to simplify greatly the analysis of large time-stamped behavioral and physiological event records and to preserve a full data trail from raw data through all intermediate analyses to the published graphs and statistics within a single data structure. The data-analysis code harvests the data several times a day and subjects it to statistical and graphical analyses, which are automatically stored in the "cloud" and on in-lab computers. Thus, the progress of individual mice is visualized and quantified daily. The data-analysis code talks to the protocol-control code, permitting the automated advance from protocol to protocol of individual subjects. The behavioral protocols implemented are matching, autoshaping, timed hopper-switching, risk assessment in timed hopper-switching, impulsivity measurement, and the circadian anticipation of food availability. Open-source protocol-control and data-analysis code makes the addition of new protocols simple. Eight test environments fit in a 48 in x 24 in x 78 in cabinet; two such cabinets (16 environments) may be controlled by one computer.     

Ethology and psychotherapy

During the last 25 years, ethology has developed systematic and quantitative methods for studying psychiatric patients' behavior, especially nonverbal behavior. Both research results as well as theoretical considerations may be of interest and value for psychiatric interviews and psychotherapy. Direct observations of endogenously depressed patients on the ward show significant behavior changes from admission to discharge. The depressive phase is characterized by withdrawal, nonspecific gaze, looking down, little self-activity, little motor activity, and a substantial reduction of social interaction. The recovery phase is characterized by verbal and nonverbal communication, that is , nod, smile, laughter, gesticulation, help, and others. Such behaviors are primarily useful for the assessment of a patient's mental state in the ward environment. In addition, they may also contribute to the psychiatric interview and future psychotherapeutic situations. These elements are related to four basic motivation categories: relaxation, assertion, contact, and flight. The theoretical considerations include evolutionary theory, ethological theory, and regulation-deregulation theory.     

Treatment of mental illness; the use and misuse of sedation and the seclusion room

Nine hundred and thirty-nine patients admitted to the locked receiving ward in the psychiatric service of the U. S. Naval Hospital, Oakland, over a ten-month period, many of them psychotic and in an acute initial episode, were treated with an intensive group therapy program, which more appropriately should be called a therapeutic community. During this time, the ward medical officer did not put any patients in a seclusion room. Patients who did not require a locked ward were quickly transferred to the open receiving ward which was established five months after this program began. It was possible to greatly diminish the quantity of sleeping medicine prescribed and practically to eliminate the use of barbiturates given parenterally. Restraints were never used. To be dealt with in this atmosphere of candor and relative freedom seemed to evoke a responsive attitude in the patients and many of them benefited from it.